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User blog:Bubby3/BM2.3 vs R function
Here, I am going to show a version of my BM2.3 analysis, but instead of psi functions, which are ambiguous, I am going to compare it to R function (not version 2 or 2.1 of it), which is unambiguous. I am also going to start from the very beginning. I am going to define a FGH-like version of BMS (can apply to any version). The definition of BMS FGH versions is this: *If the rightmost columm is all zeroes (or has no bad part) cut it off, and then iterate the matrix n times. In symbol form, #Zn, where Z is the columm of all zeroes, becomes #[#[...#[#n]...]], where # is iterated n times. *If the matrix is empty, n = n+1 *Otherwise, foerform the step as usual, but do not change the value of n, and only copy the bad part n times. R function is being modifier so that the base function is n+1 instead of 10^n. With comparabilithty to R function, I am using BMS-FGH, where the matrix xn has a similar growth rate to the string nRm, and that ordinal can be represented elsewhere by {m}. So,here is the analysis. The left side represents BMS, and the right side represents R function. Primitive sequence system *(empty matrix) = 0 *0 = 1 *0,0 = 2 *0,0,0 = 3 *0,0,0,0 = 4 *0,0,0,0... = n *0,1 = {0} *0,1,0 = 1{0} *0,1,0,0 = 2{0} *0,1,0,0... = n{0} *0,1,0,1 = {0}{0} *0,1,0,1,0,1 = {0}{0}{0} *0,1,0,1,0,1... = {0}{0}{0}... *0,1,1 = {1} *0,1,1,0,1 = {0}{1} *0,1,1,0,1,1 = {1}{1} *0,1,1,1 = {2} *0,1,1,1,0,1,1,1 = {2}{2} *0,1,1,1,1 = {3} *0,1,1,1,1... = {n} *0,1,2 = *0,1,2,1 = {1{0}} *0,1,2,1,1 = {2{0}} *0,1,2,1,2 = *0,1,2,1,2,1,2 = *0,1,2,1,2,1,2,1,2 = *0,1,2,2 = *0,1,2,2,1,2 = *0,1,2,2,1,2,2 = *0,1,2,2,2 = *0,1,2,2,2,2 = *0,1,2,3 = } *0,1,2,3,2 = } *0,1,2,3,2,3 = } *0,1,2,3,3 = } *0,1,2,3,4 = }} *0,1,2,3,4,4 = }} *0,1,2,3,4,5 = }}} *0,1,2,3,4,5,6 = }}}} Pair sequence system *(0,0)(1,1) = {0,1} *(0,0)(1,1)(0,0) = 1{0,1} *(0,0)(1,1)(0,0)(1,0) = {0}{0,1} *(0,0)(1,1)(0,0)(1,0)(1,0) = {1}{0,1} *(0,0)(1,1)(0,0)(1,0)(2,0) = {0,1} *(0,0)(1,1)(0,0)(1,1) = {0,1} *(0,0)(1,1)(0,0)(1,1)(0,0)(1,1) = {0,1} *(0,0)(1,1)(1,0) = {1{0,1}}{0,1} *(0,0)(1,1)(1,0)(1,0) = {2{0,1}}{0,1} *(0,0)(1,1)(1,0)(2,0) = {0,1} *(0,0)(1,1)(1,0)(2,0)(2,0) = {0,1} *(0,0)(1,1)(1,0)(2,0)(3,0) = {0,1}}{0,1} *(0,0)(1,1)(1,0)(2,1)(2,0)(3,1) = {0,1}}{0,1}}{0,1} *(0,0)(1,1)(1,1) = {0,1}{0,1} *(0,0)(1,1)(1,1)(1,0) = {1{0,1}{0,1}}{0,1}{0,1} *(0,0)(1,1)(1,1)(1,0)(2,1) = {0,1}{0,1}}{0,1}{0,1} *(0,0)(1,1)(1,1)(1,0)(2,1)(2,1) = {0,1}{0,1}}{0,1}{0,1} *(0,0)(1,1)(1,1)(1,0)(2,1)(2,1)(2,0)(3,1)(3,1) = {0,1}{0,1}}{0,1}{0,1}}{0,1}{0,1} *(0,0)(1,1)(1,1)(1,1) = {0,1}{0,1}{0,1} *(0,0)(1,1)(1,1)(1,1)(1,1) = {0,1}{0,1}{0,1}{0,1} *(0,0)(1,1)(1,1)(1,1)(1,1)(1,1) = {0,1}{0,1}{0,1}{0,1}{0,1} *(0,0)(1,1)(2,0) = {1,1} *(0,0)(1,1)(2,0)(0,0)(1,1) = {1,1} *(0,0)(1,1)(2,0)(0,0)(1,1)(1,1) = {1,1} *(0,0)(1,1)(2,0)(0,0)(1,1)(2,0) = {1,1} *(0,0)(1,1)(2,0)(1,0) = {1{1,1}}{1,1} *(0,0)(1,1)(2,0)(1,0)(2,1) = {1,1}}{1,1} *(0,0)(1,1)(2,0)(1,0)(2,1)(3,0) = {1,1}}{1,1} *(0,0)(1,1)(2,0)(1,0)(2,1)(3,0)(2,0)(3,1)(4,0) = {1,1}}{1,1}}{1,1} *(0,0)(1,1)(2,0)(1,1) = {0,1}{1,1} *(0,0)(1,1)(2,0)(1,1)(1,1) = {0,1}{0,1}{1,1} *(0,0)(1,1)(2,0)(1,1)(2,0) = {1,1}{1,1} *(0,0)(1,1)(2,0)(1,1)(2,0)(1,1)(2,0) = {1,1}{1,1}{1,1} *(0,0)(1,1)(2,0)(2,0) = {2,1} *(0,0)(1,1)(2,0)(2,0)(2,0) = {3,1} *(0,0)(1,1)(2,0)(3,0) = ,1} *(0,0)(1,1)(2,0)(3,1) = ,1} *(0,0)(1,1)(2,0)(3,1)(0,0)(1,1)(2,0)(3,1) = ,1}} ,1} *(0,0)(1,1)(2,0)(3,1)(1,0) = {1 ,1}} ,1} *(0,0)(1,1)(2,0)(3,1)(1,0)(2,1)(3,0)(4,1) = ,1}} ,1}} ,1} *(0,0)(1,1)(2,0)(3,1)(1,1) = {0,1} ,1} *(0,0)(1,1)(2,0)(3,1)(1,1)(2,0)(3,1) = ,1} ,1} *(0,0)(1,1)(2,0)(3,1)(2,0) = {1 ,1} *(0,0)(1,1)(2,0)(3,1)(2,0)(3,1) = ,1} *(0,0)(1,1)(2,0)(3,1)(3,0)(3,0) = ,1} *(0,0)(1,1)(2,0)(3,1)(3,0)(4,0) = ,1} *(0,0)(1,1)(2,0)(3,1)(3,0)(4,1) = {0,1}},1} *(0,0)(1,1)(2,0)(3,1)(3,0)(4,1)(4,0)(5,1) = {0,1}}{0,1}},1} *(0,0)(1,1)(2,0)(3,1)(3,1) = ,1} *(0,0)(1,1)(2,0)(3,1)(3,1)(1,1)(2,0)(3,1)(3,1) = ,1} ,1} *(0,0)(1,1)(2,0)(3,1)(3,1)(2,0) = {1 ,1} *(0,0)(1,1)(2,0)(3,1)(3,1)(2,0)(3,1)(3,1) = ,1} *(0,0)(1,1)(2,0)(3,1)(3,1)(3,0) = ,1} *(0,0)(1,1)(2,0)(3,1)(3,1)(3,0)(4,1)(4,1) = {0,1}{0,1}},1} *(0,0)(1,1)(2,0)(3,1)(3,1)(3,1) = ,1} *(0,0)(1,1)(2,0)(3,1)(4,0) = ,1} *(0,0)(1,1)(2,0)(3,1)(4,0)(3,1) = ,1} *(0,0)(1,1)(2,0)(3,1)(4,0)(3,1)(4,0) = ,1} *(0,0)(1,1)(2,0)(3,1)(4,0)(4,0) = ,1} *(0,0)(1,1)(2,0)(3,1)(4,0)(5,0) = ,1} *(0,0)(1,1)(2,0)(3,1)(4,0)(5,1) = ,1}},1} *(0,0)(1,1)(2,0)(3,1)(4,0)(5,1)(6,0)(7,1) = ,1}},1}},1} *(0,0)(1,1)(2,1) = ,1}} ,1}{{0,1},1} *(0,0)(1,1)(2,1)(1,1)(2,1) = {{0,1},1}{{0,1},1} Category:Blog posts